Simplify; express your answer in exponential form. Assume $z\neq 0, a\neq 0$. $\dfrac{{(z^{-4}a^{-5})^{-5}}}{{(za^{-3})^{-4}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(z^{-4}a^{-5})^{-5} = (z^{-4})^{-5}(a^{-5})^{-5}}$ On the left, we have ${z^{-4}}$ to the exponent ${-5}$ . Now ${-4 \times -5 = 20}$ , so ${(z^{-4})^{-5} = z^{20}}$ Apply the ideas above to simplify the equation. $\dfrac{{(z^{-4}a^{-5})^{-5}}}{{(za^{-3})^{-4}}} = \dfrac{{z^{20}a^{25}}}{{z^{-4}a^{12}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{20}a^{25}}}{{z^{-4}a^{12}}} = \dfrac{{z^{20}}}{{z^{-4}}} \cdot \dfrac{{a^{25}}}{{a^{12}}} = z^{{20} - {(-4)}} \cdot a^{{25} - {12}} = z^{24}a^{13}$